My daughter many times would only take one breast, or I would latch her on to the other and she might nurse for a minute and fall asleep.
I did 1 of 2 things. 1. I just started with the second breast the next time.
2. when my supply started getting out of control I would pump the other breast while she was nursing, then when I switched her over she was at the very least getting hind milk for the minute or 2 that she stayed awake on the other breast. I liked this way better because she would sleep for more than 15-30 minutes between the feedings